Six machines at a certain factory operate at the same constant rate.

Question

Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

A: 9
B: 12
C: 16
D: 18
E: 24

A: 9 
B: 12
C: 16
D: 18
E: 24

bbear · Accepted Answer

Suppose each machine finishes a job in x hours. This would mean that each machine has a rate of  \frac{1}{x}  jobs/hour. Using the equation R*T=Work, we can figure out the rest.

We know that four machines combined would work four times as fast as just one machine working alone. Thus, the combined rate of 4 machines is  \frac{4}{x} . Furthmore the time it takes to complete the order is 27 hours. Now we can put the complete order in terms of x:

R * T = Work 
 \frac{4}{x} * 27 = Work 
 Work = \frac{4*27}{x}

Note that I didn't do out the actual multiplication. There's no time on the actual GMAT!

Next, let's look at 6 machines. Working together, they have a rate of  \frac{6}{x} . From before, we know the order size is  \frac{4*27}{x} . We need to figure out the new time.

\frac{6}{x} * T = \frac{4*27}{x} 
 T = \frac{4}{6}*27 = \frac{2}{3}*27 = 18  (**Note that the x's cancel)

Thus, the difference is 27-18 = 9 hours, which is answer choice A.

Abhishek009 · Answer

Total work = 27 * 4

Time taken when 6 machines work =  \frac{(27*4)}{6}  => 18 hours

So, working together 6 machines take 9 hours less ( 27 - 18 )
 
Answer will be (A)

gracie · Answer

6t=4*27
t=18 hours
27-18=9 fewer hours

Bunuel · Answer

This is a copy of the following OG question: five-machines-at-a-certain-factory-operate-at-the-same-constant-rate-219084.html

Skywalker18 · Answer

Time taken by 4 machines to fill a certain production order = 27 hours
Time taken by 1 machine to fill that production order = 27 * 4 = 108 hours
Time taken by 6 machines to fill that production order = 108/6 = 18 hours

Number of fewer hours it takes 6 machines to fill that production order = 27 - 18 = 9 hours
Answer A

mohshu · Answer

given 4 machines can complete the job in 27 hrs, 
--> rate of 4 machines = 1/27
--> rate of each machine = (1/27)/4
--> rate of 6 machines = 6 * ( (1/27)/4 )= 1/18
hence , time taken by 6 machines = 18 hrs 
difference = 27 - 18 = 9
option A

yosita18 · Answer

gracie · Answer

1/(4*27)=1/108=rate of 1 machine
let t=time
t*6*(1/108)=1
t=18
27-18=9

hemantbafna · Answer

Time taken my 4 machines= 27 hours.

As the efficiencies of the machines are equal, we can take the time taken by one machine and multiply it by the time taken 4 machines we get the total hours taken by all of them.

So we can find the time taken by 1 machine= 27*4=108 hours. That is basically the time effort of 4 machines will be required by the single machine to complete the work.

6 machines will require= 108/6=18 hours.

More time required by 6 machines=27-18=9 hours.
 A

Gauriii · Answer

We can use chain formula here-
P1*D1*H1= P2*D2*H2 where, P D H are person, days and hours respectively.
6*x= 4*27 , ignoring the D since no days are given.
solving for x, we get x=18 hours.

But STOP here and re read the Q again. It says how much LESS time, not how much TIME.
Hence less time = 27-18=9 hours

m7runner · Answer

If 4 machines take a total of 27 hours to complete a production order, then 1 machine will take  27*4 = 108  hours to complete a production order.

Therefore, 6 machines will take  \frac{108}{6} = 18  hours.

Difference in number of hours taken by 6 machines vs 4 machines in fulfilling a production order =  27-18 = 9  hours.

Answer choice (A) is correct, IMO.

TargetMBA007 · Answer

I get the correct answer, when I find the speed of 6 machines by doing 6/27*4 = 1/18, hence 18 hours, and then minus 9 hours.
However, if I directly do:
6/(27*4)-(1/27), it produces = 1/54, or 54 hours. I wonder, what is fundamentally the error with the second approach?

KarishmaB

KarishmaB · Answer

Recall that we can easily solve these questions using the concept of Joint variation:

4.................27
6................. ??

T = 27 * (4/6) 
because time taken will reduce when number of machines increases

T = 18 i.e. time taken will be 9 hrs less

In your second approach, you are calculating 'Rate of 6 machines - Rate of 4 machines' which gives you 'Rate of 2 machines' since rates are additive. 
(you know Rate of 4 machines + Rate of 2 machines = Rate of 6 machines)

So 1/54 is the rate of 2 machines and 54 hrs is the time taken when only 2 machines are working. What we are actually asked is the simple subtraction 'time taken by 4 machines - time taken by 6 machines'

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Six machines at a certain factory operate at the same constant rate.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Six machines at a certain factory operate at the same constant rate.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards